Isn’t the concept of zero self evident? If I am in an ancient hunter and gather society and someone asks me how many wooly mammoths I killed that day, wasn’t there a way to express that I killed none?
The concept of none is obvious. The concept of zero as an operator in mathematics isn’t.
For example, while addition and subtraction make easy use of zero, multiplication and division require far more sophisticated handling. Ten times one is the same as ten divided by one. What is zero times ten? Is it the same as zero times one? Why or why not? What is ten divided by zero? What is zero times zero, for that matter? Or zero raised to the zeroth power? Put zero into many types of equations and the answer is either not obvious or nonsensical.
Even as a place holder, zero is not obvious or even necessary. Roman numerals get along fine without zero. Why then introduce a seemingly unnecessary device that does more damage than any good it adds?
I understand that in complex mathematics it is non-intuitive, but the ancient hunters/gatherers wouldn’t even use it for simple things like say, the number of berries to divide amongst the members?
For example, there are ten adults in the group. We see that Xena got 4 berries, Oompa got 0, Xilda got 4, etc., add them together and then divide by ten. Did the hunters and gatherers not have even such a rudimentary understanding?
I know they were not contemplating a divide by zero problem or certainly nothing more complex, but perhaps I am being overly technical about the OP’s question.
Having “none” of something is not a concept that you have to learn. It is actually hard-wired into our brains. So is having “one” and “two” of something. The hard-wiring stops somewhere around 3 or 4, maybe 5, I don’t recall exactly. Your brain is also hard wired to have the concept of “a few”, and “many”. While at some point you learn words for these, you don’t need to learn the concepts. You are born with them.
Counting to ten is not something that you are born with. That concept has to be developed. Dividing equally is easy enough, but being able to express that with numbers is also something that has to be developed. Early hunter-gatherers probably did not have the mathematical knowledge to figure things like dividing berries up by numbers. They just divided the berries into roughly equal piles and called it a day.
Oompa almost certainly had a word to indicate that Oompa had no berries, but that word was not used for counting and was not used like a number.
Even when you get a lot more advanced than hunter-gatherers, you still didn’t usually have zero as a number. Look at Roman numerals. You can express any number in Roman numerals (well, whole numbers at least), but there’s no zero. There’s a word for zero (which Google tells me is “nulla”, I don’t speak Latin so I’ll go with that), but there’s no mathematical zero. Roman numerals start at I. If there weren’t any deaths in the Colosseum that day, Brian could certainly say that there were no deaths (assuming he wasn’t busy writing Romani ite domum C times so that he wouldn’t get his balls cut off) but he would express it as a lack of deaths rather than a number of deaths.
Even in modern English, “there were no deaths” is not using a number. While it is equivalent to “there were zero deaths”, the latter uses a number and the former does not.
I suppose that you could make the argument that the Roman number system is a method of calculation with only 1s (tally marks would better be described in that way, though).
In the 20th century, before the electric computer was invented, there was such a thing as a “computer”. It was the term for a group of women who would perform math calculations in bulk. Possibly, there were such groups in the 19th century as well, but I don’t believe that there were such groups in ancient times.
Programming comes from weaving, with patterns being encoded into a medium, which a weaving machine could read and turn into a rug with a pattern. This was, as I recall, invented in the 18th or 19th century.
You could stretch the modern meanings to cover some group of Ancient Roman group of engineering apprentices, taking the direction of their master, to design an architectural element or whatever. While I wouldn’t be surprised if something like that happened, being told to “figure out the length of the arc in this circle” isn’t really the same thing as “programming”. Programs don’t figure out, they just blindly follow very precise and unrelenting instructions, even if it takes them into hell.
Early groups didn’t need zero because they used a rudimentary form of what we today call set theory.
They started with a bunch of berries. Xena got one, then Oompa got one, then Xilda got one, then repeat until the berries are gone. Each set of berries should be the same, i.e. placeable into a one-to-one correspondence. There’s no need to divide; if the count doesn’t come out even and Xena gets an extra one this time, then the count starts with Oompa and Xilda next time.
This works even if the chief takes a larger share. Xena can get two for every one Oompa and Xilda get, for example. Or Xena can get two handfuls for every one berry otherwise distributed. You can get amazingly sophisticated with sets.
But at no time do they ever say - or need to say - that Xena gets one for every zero that the outcast Zog gets. Zog’s nothing is not part of the count. The concept of none is there, but not the mathematical concept of zero. The null set is a device that took millennia to invent.
Zero as a null set is a level up from the concept of none. One is math, the other isn’t.
Though we don’t know who discovered zero, we do know who was first saved by zero.
It may seem very self-evident to us, but it seems reasonable to me that there is a big jump between the verb “I didn’t kill any” and the quantity “I killed zero”.
A couple of posters have mentioned Seife’s book. I bought it several years ago and found it fascinating. I’ve reread it a few times since then. Check it out at Amazon: Zero: The Biography of a Dangerous Idea Paperback – by Charles Seife (Don’t forget to try Amazon’s “Look Inside” feature, to read parts of it!)
Yes, because at that point you are beginning to understand the mathematical concept of a number, not merely counting corpses. Then it is a slippery slope down to negative numbers, irrationals, and killing things using fuel-air explosives and thermonuclear bombs instead of spears.
I agree with this.